in silico Plants

Reduced cortical cell files (CCFN) and enlarged cortical cells (CCS) reduce root maintenance costs. We used OpenSimRoot, a functional-structural model, to test the hypothesis that larger CCS, reduced CCFN, and their interactions with root cortical aerenchyma (RCA), are useful adaptations to suboptimal soil N, P, and K availability. Interactions of CCS and CCFN with lateral root branching density (LRBD) and increased carbon availability were evaluated under limited N, P and K availability. The combination of larger CCS and reduced CCFN increases the growth of maize up to 105%, 106%, and 144%, respectively, under limited N, P, or K availability. Interactions among larger CCS, reduced CCFN, and greater RCA results in combined growth benefits of up to 135%, 132%, and 161% under limited N, P, and K levels, respectively. Under low phosphorus and potassium availability, increased LRBD approximately doubles the utility of larger CCS and reduced CCFN. The utility of larger CCS and reduced CCFN is reduced by greater C availability as may occur in future climate scenarios. Our results support the hypothesis that larger CCS, reduced CCFN, and their interactions with RCA could increase nutrient acquisition by reducing root respiration and root nutrient demand. Phene synergisms may exist between CCS, CCFN, and LRBD. Natural genetic variation in CCS and CCFN merit consideration for breeding cereal crops with improved nutrient acquisition, which is critical for global food security.One sentence summary Functional-structural modeling indicates that enlarged root cortical cells and reduced cortical cell file number decrease root maintenance cost, permitting greater soil exploration, resource capture, and plant growth under suboptimal nitrogen, phosphorus and potassium availability.Abbreviations(CCS)Cortical cell size(CCFN)Cortical cell file number(RCA)Root cortical aerenchyma(SCD)Steep, Cheap and Deep(LRBD)Lateral root branching density(RHL)Root hair length(BRGA)Basal root growth angleView Full Text

Constraint-based modelling was applied to provide a mechanistic understanding of the possible metabolic origins of the Kok effect - the change in quantum yield of net photosynthesis at low light intensity. The well-known change in quantum yield near the light-compensation point (LCP) was predicted as an emergent behaviour from a purely stoichiometric model. From our modelling results, we discovered another subtle change in quantum yield at a light intensity lower than the LCP. Our model predicted a series of changes in metabolic flux modes in central carbon metabolism associated with the changes in quantum yields. We demonstrated that the Kok effect can be explained by changes in metabolic flux modes between catabolism and photorespiration. Changes in RuBisCO carboxylation to oxygenation ratio resulted in a change in quantum yield at light intensities above the LCP, but not below the LCP, indicating the role of photorespiration in producing the Kok effect. Cellular energy demand was predicted to have no impact on the quantum yield. Our model showed that the Kok method vastly overestimates day respiration - the CO2 released by non-photorespiratory processes in illuminated leaves. The theoretical maximum quantum yield at low light intensity was higher than typical measured values, suggesting that leaf metabolism at low light may not be regulated to optimise for energetic efficiency. Our model predictions gave insights into the set of energetically optimal changes in flux modes in low light as light intensity increases from darkness. One sentence summaryThe Kok effect can be explained by the changes in flux modes between catabolism and photorespiration.

Large-scale kinetic models of photosynthesis enable time-resolved predictions of traits related to this key process, and provide the means to identify factors limiting photosynthesis. However, their use is currently limited by the lack of efficient approaches to estimate the hundreds of genotype-specific kinetic parameters. Here, we present C4TUNE, an artificial neural network, which can efficiently predict parameters of a large-scale photosynthesis model from photosynthesis response curves. C4TUNE was trained on a biologically-relevant synthetic dataset comprising matched samples of parameters and response curves obtained using a C4 photosynthesis kinetic model. To speed up the training of C4TUNE, we devised a surrogate neural network to predict photosynthesis response curves directly from the model parameters and environmental inputs. Given response curves as input, we showed that over 99% of the parameter vectors predicted by C4TUNE could be used directly in simulation of the kinetic model and resulted in excellent fits. Finally, we applied C4TUNE to predict parameters for a population of 68 maize genotypes across two seasons. The predicted genotype-specific parameters allowed pinpointing factors that limit photosynthetic efficiency, validated using simulations. Therefore, the use of C4TUNE presents a fast and precise approach for parameter prediction based on minimal datasets.

Engineering a novel N2-fixing rhizobia symbiosis in cereal crops is a strategy being pursued to improve agricultural sustainability. However, if such a symbiosis were introduced, it would have to be economically viable in the context of existing nutrient acquisition strategies, including the existing symbiosis with arbuscular mycorrhizal fungi (AMF) that the vast majority of plants already engage in. This raises the question of how the metabolic costs and benefits from these separate symbioses that have partially overlapping functions might impact nutrient status and subsequent plant growth. To address this, we developed metabolic models describing how the relative growth rate of Zea mays is impacted by the AMF Rhizophagus irregularis and a hypothetical N2-fixing symbiosis with Bradyrhizobium diazoefficiens both in isolation and in tandem. To validate the AMF component of our model, we conducted field evaluation of mutant AMF-incompatible maize hybrids and found that the empirically measured AMF-mediated growth benefit agreed well with our models predictions. Our model of the rhizobium symbiosis predicted that the lower N content of cereal crops makes the relative growth rate cost associated with acquiring nitrogen from N2-fixing rhizobia smaller than in legumes. Finally, our model also predicted positive synergies between rhizobia and AMF under nutrient-limited conditions but negative synergies under nutrient, particularly phosphorus, replete conditions. These findings indicate that these bioengineering strategies could improve cereal crop yields and may achieve greater gains in tandem, but soil nutrient status of target sites as well as the nitrogen requirements of specific varieties should be considered.

Deep neural networks can be trained to predict gene expression directly from genomic sequence, thereby implicitly learning regulatory sequence patterns from scratch, minimizing the bias imposed by prior assumptions. A challenging, yet promising prospect is the extraction of novel insights into gene-regulatory mechanisms, by probing and interpreting such gene expression models. Using a branched convolutional neural network architecture trained on promoter and terminator sequences we predict gene expression for allopolyploid Brassica napus and the closely related model organism Arabidopsis thaliana. We validate the model by comparing predicted and measured expression across ecotypes. We also show that deep learning models can successfully capture the positional binding preferences of some transcription factor families, without having been trained on transcription factor binding data. Furthermore, we show that our model did not only detect local sequence patterns, but was also able to determine their function based on their positional context. We also found that increased prediction error correlated with additional more distal or epigenetic regulatory input. Our results demonstrate that deep learning can be used to understand the regulatory architecture of gene expression in plants. A better understanding of gene regulation in the context of polyploid genomes is of particular economic importance, due to their prevalence among major crops. In the future, we hope that such models may facilitate the targeted engineering of gene regulation in crops.

Genomic selection and gene editing in crops could be enhanced by multi-species, mechanistic models predicting effects of changes in gene regulation. Current expression abundance prediction models require extensive computational resources, hard-to-measure species-specific training data, and often fail to incorporate data from multiple species. We hypothesize that gene expression prediction models that harness the regulatory network structure of Arabidopsis thaliana transcription factor-target gene interactions will improve on the present maize models. To this end, we collect 147 Oryza sativa and 99 Sorghum bicolor gene expression assays and assign them to maize family-based orthologous groups. Using three popular graph-based machine learning frameworks, including a shallow graph convolutional autoencoder, a deep graph convolutional autoencoder, and the inductive GraphSage strategy, we encode an Arabidopsis thaliana integrated gene regulatory network (iGRN) structure and TF gene expression values to predict gene expression both within and between species. We then evaluate the network methods against a partial least-squares baseline. We find that the baseline gives the best predictions within species, with Spearman correlations averaging between 0.74 and 0.78. The graph autoencoder methods were more variable with correlations between -0.1 and 0.65. In particular, the GraphSage and deep autoencoders performed the worst, and the shallow autoencoders performed the best. In the most challenging prediction context, where predictions were in new species and on genes that were not seen, we found that the shallow graph autoencoder framework averaged around 0.65. Unlike initial thoughts about preserved network structure improving gene expression predictions, this study shows that within-species predictions only need simple models, such as partial least squares, to capture expression variations. In cross-species predictions, the best model is often a more complex strategy utilizing regulatory network structure and other studies expressions.

Grasses grow a series of phytomers during development. The distance between successive leaves is determined by internode lengths. Grasses exhibit genetic, developmental, and environmental variability in phytomer number, but how this affects internode length, biomass, and height is unknown. We hypothesized that a generalized mathematical model of phytomer development wherein between-phytomer competition influences internode length distributions would be sufficient to explain internode length patterns in two Setaria genotypes: weedy A10 and domesticated B100. Our model takes a novel approach that includes the vegetative growth of leaf blade, sheath, and internode at the individual phytomer level, and the shift to reproductive growth. To validate and test our mathematical model, we carried out a greenhouse experiment. We found that the rate of leaf emergence is consistent for both genotypes across development, and that the length of time spent elongating for the leaf and internode can be described as the ratio between the time of phytomer emergence and the elongation completion time. The validated model was simulated across all possible parameter values to predict the influence of phytomer number on internode length. This analysis predicts that different internode length distributions across different numbers of total phytomers are an emergent property, rather than a genotype-specific property requiring genotype-specific models. We applied the model to internode length only field data of S. italica accession B100, grown under both well-watered and drought conditions. The model predicts that droughted plants reduce leaf elongation time, reduce resource allocation to the internodes, and overall experience slower growth. Together, model and data suggest that allometric patterns are driven by competition for resources among phytomer and the shift to reproductive growth in Setaria. The resulting model enables us to predict growth dynamics and final allometries at the phytomer level.

Development and spatial pattern formation are inherently linked. The coordinated determination of cell fates is crucial in any developmental process and requires extensive intercellular communication. Plants cells exchange many molecular signals via the symplasmic pathway, i.e., via plasmodesmata: narrow channels connecting the cytoplasm of neighbouring cells. Regulation of symplasmic transport is vital for normal plant development, and mutations that disrupt this regulation are often embryo or seedling lethal. In many tissues, symplasmic transport of small molecules is diffusion driven, resulting in a non-selective and bidirectional transport, although net directionality could arise from gradients. This has led to the (dogmatic) belief that symplasmic transport can only be detrimental to pattern formation, because signalling molecules cannot be confined, and gradients would fade. Here, we develop a detailed biophysical description of symplasmic transport to explore how plasmodesmata affect gradients in a linear tissue. We then apply the model in more complex tissue contexts, observing and explaining, e.g., that symplasmic transport may result in steeper gradients in the root apical meristem. In conclusion, our model provides a reference framework for estimating the consequences of symplasmic transport and explains how symplasmic transport can contribute to more robust developmental patterning.

Photosynthetic manipulation provides new opportunities for enhancing crop yield. However, understanding and quantifying effectively how the seasonal growth and yield dynamics of target crops might be affected over a wide range of environments is limited. Using a state-of-the-art cross-scale model we predicted crop-level impacts of a broad list of promising photosynthesis manipulation strategies for C3 wheat and C4 sorghum. The manipulation targets have varying effects on the enzyme-limited (Ac) and electron transport-limited (Aj) rates of photosynthesis. In the top decile of seasonal outcomes, yield gains with the list of manipulations were predicted to be modest, ranging between 0 and 8%, depending on the crop type and manipulation. To achieve the higher yield gains, large increases in both Ac and Aj are needed. This could likely be achieved by stacking Rubisco function and electron transport chain enhancements or installing a full CO2 concentrating system. However, photosynthetic enhancement influences the timing and severity of water and nitrogen stress on the crop, confounding yield outcomes. Strategies enhancing Ac alone offers more consistent but smaller yield gains across environments, Aj enhancement alone offers higher gains but is undesirable in less favourable environments. Understanding and quantifying complex cross-scale interactions between photosynthesis and crop yield will challenge and stimulate photosynthesis and crop research. Summary StatementLeaf-canopy-crop prediction using a state-of-the-art cross-scale model improves understanding of how photosynthetic manipulation alters wheat and sorghum growth and yield dynamics. This generates novel insights for quantifying impacts of photosynthetic enhancement on crop yield across environments.

Computational modelling has become essential to advancing our understanding of plant developmental and physiological processes, necessitating the development of new computational approaches and software. Here, we present VirtualLeaf-2.0, an updated version of this modelling framework for the biophysical and biomechanical interactions between cells in plant tissues, with novel features for more detailed modelling of the cell wall. In particular, the updated version of VirtualLeaf enables detailed modelling of variations in cell wall stability and cell wall sliding up to the level of individual cell wall elements. The plant cell wall plays a pivotal role in plant development and survival, with younger cells generally having thinner, more flexible (primary) walls than older cells. Cell wall stability is further affected by signalling in growth processes and pathogen infection. The improvements of VirtualLeaf lay the groundwork for using VirtualLeaf to address novel questions involving plant tissue dynamics during growth, tissue formation and pathogen defence, as illustrated with example simulations.

Increasing winter temperatures jeopardize the yield of fruit trees requiring a prolonged and sufficiently cold winter to flower. Assessing the exact risk to different crop varieties is the first step in mitigating the harmful effect of climate change. Since empirically testing the impacts of many temperature scenarios is very time-consuming, quantitative predictive models could be extremely helpful in reducing the number of experiments needed. Here, we focus on olive (Olea europaea) - a traditional crop in the Mediterranean basin, a region expected to be severely affected by climatic change. Olive flowering and consequently yield depend on the sufficiency of cold periods and the lack of warm ones during the preceding winter. Yet, a satisfactory quantitative model forecasting its expected flowering under natural temperature conditions is still lacking. Previous models simply summed the number of cold hours during winter, as a proxy for flowering, but exhibited only mediocre agreement with empirical flowering values, possibly because they overlooked the order of occurrence of different temperatures. We empirically tested the effect of different temperature regimes on olive flowering intensity and flowering-gene expression. To predict flowering based on winter temperatures, we constructed a dynamic model, describing the response of a putative flowering factor to the temperature signal. The crucial ingredient in the model is an unstable intermediate, produced and degraded at temperature-dependent rates. Our model accounts not only for the number of cold and warm hours but also for their order. We used sets of empirical flowering and temperature data to fit the model parameters, applying numerical constrained optimization techniques, and successfully validated the model outcomes. Our model more accurately predicts flowering under winters with warm periods yielding low-to-moderate flowering and is more robust compared to previous models. This model is the first step toward a practical predictive tool, applicable under various temperature conditions.

Drought is a significant factor in agricultural losses, making it imperative to understand how root system architecture (RSA) adapts to environmental condition like water deficit. HydroRoot is a functional-structural plant model (FSPM) aimed at analyzing and simulating hydraulic and solute transport of RSA. The model integrates a static hydraulic solver, a coupled water-solute transport solver, a statistical generator of RSA based on Markov model, and a dynamic hydraulic model accounting for root growth. This paper presents the model, the mathematical description of the formalism of solvers, and use cases with their associated tutorials. Five use cases illustrate capabilities of HydroRoot, which has been successfully used for phenotyping root hydraulics across various species, including Arabidopsis, maize, and millet. The model-driven phenotyping method "cut and flow" is presented to characterize axial and radial conductivities on a given root genotype. Finally, three step-by-step tutorials provide a structured way to learn how to use HydroRoot 1) to simulate hydraulic on a given architecture, 2) to simulate water and solute transport on a maize root, and 3) to simulate hydraulic on two pearl millet genotypes with varying soil conditions. Hydroroot is an open-source package of the OpenAlea platform, with the code publicly available on Github. A comprehensive documentation is available with a reproducible gallery of examples.

Integrated root phenotypes contribute to environmental adaptation and yield stability. We used the functional-structural plant/soil model OpenSimRoot_v2 to reconstruct the root phenotypes and environments of eight maize landraces to understand the phenotypic and environmental factors associated with broad adaptation. We found that accessions from low phosphorus regions have root phenotypes with shallow growth angles and greater nodal root numbers, allowing them to adapt to their native environments by improved topsoil foraging. We used machine learning algorithms to detect the most important phenotypes responsible for adaptation to multiple environments. The most important phene states responsible for stability across environments are large cortical cell size and reduced diameter of roots in nodes 5 and 6. When we dissected the components of root diameter, we observed that large cortical cell size improved growth by 28%, 23 % and 114%, while reduced cortical cell file number alone improved shoot growth by 137%, 66% and 216%, under drought, nitrogen and phosphorus stress, respectively. Functional-structural analysis of 96 maize landraces from the Americas, previously phenotyped in mesocosms in the greenhouse, suggested that parsimonious anatomical phenotypes, which reduce the metabolic cost of soil exploration, are the main phenotypes associated with adaptation to multiple environments, while root architectural traits were related to adaptation to specific environments. Our results indicate that integrated phenotypes with root anatomical phenes that reduce the metabolic cost of soil exploration will increase tolerance to stress across multiple environments and therefore improve yield stability, regardless of their root architecture.

O_LIBackground and Aims Functional-structural plant models are increasingly being used by plant scientists to address a wide variety of questions. However, the calibration of these complex models is often challenging, mainly because of their high computational cost. In this paper, we applied an automatic method to the calibration of WALTer: a functional-structural wheat model that simulates the plasticity of tillering in response to competition for light. C_LIO_LIMethods We used a Bayesian calibration method to estimate the values of 5 parameters of the WALTer model by fitting the model outputs to tillering dynamics data. The method presented in this paper is based on the Efficient Global Optimisation algorithm. It involves the use of Gaussian process metamodels to generate fast approximations of the model outputs. To account for the uncertainty associated with the metamodels approximations, an adaptive design was used. The efficacy of the method was first assessed using simulated data. The calibration was then applied to experimental data. C_LIO_LIKey Results The method presented here performed well on both simulated and experimental data. In particular, the use of an adaptive design proved to be a very efficient method to improve the quality of the metamodels predictions, especially by reducing the uncertainty in areas of the parameter space that were of interest for the fitting. Moreover, we showed the necessity to have a diversity of field data in order to be able to calibrate the parameters. C_LIO_LIConclusions The method presented in this paper, based on an adaptive design and Gaussian process metamodels, is an efficient approach for the calibration of WALTer and could be of interest for the calibration of other functional-structural plant models. C_LI

Root system architecture (RSA) is central to plant adaptation and fitness, yet the design principles and regulatory mechanisms connecting RSA to environmental adaptation are not well understood. We developed Ariadne, a semi-automated software for quantifying cost-efficiency tradeoffs of RSA by mapping root networks onto a Pareto-optimality framework, which describes the balance between resource transport efficiency and construction cost. Applying Ariadne to Arabidopsis thaliana, we found that root architectures consistently assume Pareto-optimal forms across developmental stages, genotypes, and environmental conditions. Using the Discovery Engine, an engine that combines machine learning together with interpretability techniques, we found developmental stage, the hy5/chl1-5 genotype, and manganese availability as important determinants of the cost-efficiency tradeoff, with manganese exerting a unique influence not observed for other nutrients. These results reveal that RSA plasticity is genetically constrained to cost-efficiency optimal configurations and that developmental and environmental factors shift RSA on the pareto front, with manganese acting as a strong modulator of the transport efficiency and construction cost balance.

Efforts to cope with hunger by breeding highly productive annual crops for rain-fed agriculture in stochastic-rainfall environments have had only minor success, which we attribute to biological constraints that limit the crops yields. We use optimization modelling to interpret experimentally measured transpiration trajectories of wild barley plants following a rain event: the plants first maximized biomass accumulation by employing their maximal transpiration rate, then switched to their minimal transpiration rate to ensure survival until maturity. Thus, breeding plants with lower minimal transpiration rates combined with higher water-use efficiency and maximal transpiration rates could increase expected yields. However, our experimental results indicate that biological constraints impose tradeoffs among maximal and minimal transpiration rates and water-use efficiency. A proposed breeding methodology identifies less biologically constrained cultivar candidates.

Evolutionary studies indicate that species in stable environments often evolve with reduced plasticity, whereas those in variable environments tend to maintain higher plasticity to adapt to changing conditions. Our study explores whether this evolutionary principle extends to cultivated crops. In crop science, phenotypic plasticity is generally understood as a short-term response to environmental factors. Yet, the long-term evolutionary changes in both plastic and non-plastic traits under different cultivation regimes remain largely unexamined. Herein, we developed a novel mechanistic crop growth model, collectively termed the Trait-Environment Fitness Interaction (TEFI) Model, to study if and how trait plasticity varies among crops under different cultivation regimes. Our results, based on the TEFI Model, show higher trade-offs between fitness and plasticity. Specifically, we observed the evolution of higher plasticity in crops subjected to intermittent cultivation, which experienced more variable environments. However, this higher plasticity does not compensate for fitness losses due to the high rate of environmental unpredictability. Conversely, species under relatively stable conditions tend to evolve with reduced plasticity. Using real-world crop datasets, we validated the theoretical predictions of the TEFI Model, which suggest that the longer the interruption, the higher the plasticity. Our results highlight the evolutionary impact of cultivation patterns on trait plasticity and its importance in crop fitness. Ultimately, our findings illustrate how evolutionary principles of plasticity, as captured by the TEFI Model, can inform sustainable crop improvement strategies.

Plant growth and development involve the integration of numerous processes, influenced by both endogenous and exogenous factors. At any given time during a plants life cycle, the plant architecture is a readout of this continuous integration. However, untangling the individual factors and processes involved in the plant development and quantifying their influence on the plant developmental process is experimentally challenging. Here we used a combination of computational plant models to help understand experimental findings about how local phloem anatomical features influence the root system architecture. In particular, we simulated the mutual interplay between the root system architecture development and the carbohydrate distribution to provide a plausible mechanistic explanation for several experimental results. Our in silico study highlighted the strong influence of local phloem hydraulics on the root growth rates, growth duration and final length. The model result showed that a higher phloem resistivity leads to shorter roots due to the reduced flow of carbon within the root system. This effect was due to local properties of individual roots, and not linked to any of the pleiotropic effects at the root system level. Our results open the door to a better representation of growth processes in plant computational models.

The conversion of supplemental greenhouse light energy into biomass is not always optimal. Recent trends in global energy prices and discussions on climate change highlight the need to reduce our energy footprint associated with the use of supplemental light in greenhouse crop production. This can be achieved by implementing "smart" lighting regimens which in turn rely on a good understanding of how fluctuating light influences photosynthetic physiology. Here, a simple fit-for-purpose dynamic model is presented. It accurately predicts net leaf photosynthesis under natural fluctuating light. It comprises two ordinary differential equations predicting: 1) the total stomatal conductance to CO2 diffusion and 2) the CO2 concentration inside a leaf. It contains elements of the Farquhar-von Caemmerer-Berry model and the successful incorporation of this model suggests that for tomato (Solanum lycopersicum L.), it is sufficient to assume that Rubisco remains activated despite rapid fluctuations in irradiance. Furthermore, predictions of the net photosynthetic rate under both 400ppm and enriched 800ppm ambient CO2 concentrations indicate a strong correlation between the dynamic rate of photosynthesis and the rate of electron transport. Finally, we are able to indicate whether dynamic photosynthesis is Rubisco or electron transport rate limited. Author summaryThe cultivation of greenhouse crops under optimised conditions will become increasingly important, with supplemental lighting playing a vital role. However, converting light energy into plant photosynthesis is not always optimal. A potential venue that may lead to the efficient conversion of light energy involves a model-based implementation of "smart" lighting control strategy. This approach does however necessitate a good understanding of how plants harness light energy under natural fluctuating irradiance. Accordingly, as a first step, we have developed a small leaf-level model that predicts dynamic photosynthesis in natural fluctuating light. It may potentially be used in future supplemental light control applications.

Predicting the phenotype from the genotype is one of the major contemporary challenges in biology. This challenge is greater in plants because their development occurs mostly post-embryonically under diurnal and seasonal environmental fluctuations. Current phenotype prediction models do not adequately capture all of these fluctuations or effectively use genotype information. Instead, we have developed a dynamic modular approach that captures the genotype, environment, and Genotype-by-Environment effects to express the time-to-flowering phenotype in real time in Phaseolus vulgaris. The module we describe can be applied to different plant processes and can gradually replace processes in existing crop models. Our model can enable accelerated progress in diverse breeding programs, particularly with the prospects of climate change. Finally, a gene-based simulation model can assist policy decision makers in matters pertaining to prediction of food supplies.